a. Model the situation with an exponential function. The exponential function that models the problem in this case is: y = 1056 (1.28) ^ t Where, t: number of years
b. Find how many alligators there will be in 8 years. For 8 years we must replace the value of t = 8 in the written equation. We have then: y = 1056 (1.28) ^ 8 y = 7609.28193 Nearest whole integer: y = 7609
c. How many years will it take for the population to become 3000?
For this we should almost replace y = 3000 in the equation of part A. We have then: 3000 = 1056 (1.28) ^ t From here, we clear t: (1.28) ^ t = (3000) / (1056) We apply logarithm to both sides: log1.28 ((1.28) ^ t) = log1.28 ((3000) / (1056)) t = log1.28 ((3000) / (1056)) t = 4.229619111 years.
